On Tuesday, November 22, 2022 at 2:40:09 PM UTC-6 jessem wrote: > One result that might lend itself to a hypothetical frequentist take on QM > probabilities is discussed by David Z Albert on p. 237-238 of the book The > Cosmos of Science, those pages can be read at > https://books.google.com/books?id=_HgF3wfADJIC&lpg=PP1&pg=PA238#v=onepage&q&f=false > > . He considers a scenario where a measuring device is interacting with an > infinite series of identically prepared quantum systems, and creating a > "pointer state" that tells you just the fraction of those systems that > showed a certain result (like an electron being spin-up), and he considers > what happens if we analyze this scenario without invoking the collapse > postulate or the Born rule, instead just modeling the measurements as > entanglement between the measuring system and the system being measured. > After a finite number of trials the pointer will be in a superposition of > states, but in the infinite limit, all the amplitude becomes concentrated > on the eigenstate of the pointer measurement operator where the pointer > shows the correct quantum-mechanical probability (for example, "1/2 of all > trials showed spin-up"). > > This type of collapse-free derivation of something like probability in the > infinite limit is also discussed in section 5 of the paper at > https://www.academia.edu/6975159/Quantum_dispositions_and_the_notion_of_measurement > > starting on p. 12, apparently the result is known as "Mittelstaedt's > theorem". I suppose this result can't really explain why we seem to see > definite outcomes (as opposed to superpositions) after a finite number of > trials without some additional QM interpretation, but it at least has a > "flavor" reminiscent of hypothetical frequentism. > > I am not one to engage a lot in these arguments. I see quantum mechanics has having a limited number of postulates. These are:
Quantum amplitudes are complex valued and have modulus squares that are probabilities. Observable outcomes are the eigenvalues of Hermitian or self-adjoint operators Aψ = aψ. Transformations of quantum states and their evolution are defined by unitary operators ψ' = Uψ and ψ(t) = U(t)ψ(0), which are generated by self-adjoint operators. The Born rule, which is similar to the Euclid 5th axiom in that people think it should be provable from the other 3 axioms. Whether QM is Bayesian or frequentist is rather related to the question of whether it is ψ-epistemic or ψ-ontic respectively. I do not think either stance is provable within the structure of QM, or observable by experimentation. The Copenhagen and Qubism interpretations are ψ-epistemological while the Everettian Many Worlds, transactional, Bohm and some others are ψ-ontological interpretations. Which ever one you want you can freely choose. I have some rather deep ideas about this with respect to the unprovability of quantum interpretations. LC > On Tue, Nov 22, 2022 at 10:54 AM Lawrence Crowell < > [email protected]> wrote: > >> There are two concepts of probability and statistics, Bayesianism and >> frequentism (orthodox view), which formulate probability in somewhat >> different ways. I would say that quantum mechanics might be the most >> rigorous definition of probability. I would be tempted to say it is more >> Bayesian than frequentist. >> >> LC >> >> On Monday, November 21, 2022 at 8:15:19 PM UTC-6 [email protected] wrote: >> >>> On 22-11-2022 02:47, Brent Meeker wrote: >>> > On 11/21/2022 5:12 PM, smitra wrote: >>> >> The problem lies with the notion of probability, he explains here >>> that >>> >> it cannot refer to anything in the physics world as an exact >>> >> statement: >>> >> >>> >> https://www.youtube.com/watch?v=wfzSE4Hoxbc&t=1036s >>> >> >>> >> That's then a problem for a fundamental theory of physics as such a >>> >> theory must refer to statements about nature that are exactly true. >>> > >>> > Who says so? Physics never makes exact measurements. Why should the >>> > theory do something that the physics can't? Deutsch is like the >>> > scholastics, he thinks physics is just a branch of mathematical logic. >>> > >>> > Brent >>> >>> But physics cannot implement a rigorous notion of probability. So, that >>> then makes QM in the traditional formulation problematic. >>> >>> Saibal >>> >> -- >> > You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> > To view this discussion on the web visit >> https://groups.google.com/d/msgid/everything-list/54ebbfed-1a27-4b4e-bcc1-0cdf1186398bn%40googlegroups.com >> >> <https://groups.google.com/d/msgid/everything-list/54ebbfed-1a27-4b4e-bcc1-0cdf1186398bn%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/203a9a94-4896-436d-95a2-eac6d80859b0n%40googlegroups.com.
